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lfunc_lfunctions • Show schema
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{'Lhash': '1599888217125868594429030592002', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.5731321849709863, -0.724744871391589], 'a4': [0.0, 0.0], 'a5': [1.224744871391589, 0.7071067811865476], 'a6': [0.0, 0.0], 'a7': [0.2679491924311227, 0.0], 'a8': [0.0, 0.0], 'a9': [1.949489742783178, -2.2802389661575337], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.282356664340774, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.5731321849709863, 0.724744871391589]]], [19, [[1.0, 0], [1.7320508075688772, -4.0]]]], 'bad_primes': [2, 3, 19], 'central_character': '912.65', 'coefficient_field': 'CDF', 'conductor': 912, 'conductor_radical': 114, 'conjugate': '2018568927218427713403070766613', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.5731321849709863, 0.724744871391589]], [[1.0, 0], [-1.224744871391589, -0.7071067811865476], [2.5, 4.330127018922194]], [[1.0, 0], 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'primitive': True, 'rational': False, 'root_analytic_conductor': 2.698584196266771, 'root_angle': -0.038506678713639816, 'root_number': '0.9926917705340853 - 0.12067745735597417*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0192533393568', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.26208926721434338163630284158', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.79564905164361778775530653270', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.46941770451879592166586638229', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.282356664340774, 'bad_primes': [2, 3, 19], 'central_character': '57.8', 'conductor': 912, 'conductor_radical': 114, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/912/2/bn/m/65/4'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-912-57.8-c1-0-18', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-912-57.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.698584196266771, 'root_angle': -0.019253339356819908, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.26208926721434338163630284158', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1599888217125868594429030592002', 'Lhash_array': ['1599888217125868594429030592002'], 'label': '2-912-57.8-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/912/2/bn/m/65/4'}